9Vehiclerouting2009

# 9Vehiclerouting2009 - Prof.Dr Fsun lengin Fusun Ulengin 1 Vehicle Routing Separate single origin and destination Once we have selected transport

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Prof.Dr. Füsun Ülengin 1 Fusun Ulengin

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Vehicle Routing: Separate single origin and destination: Once we have selected transport mode and have goods that need to go from point A to point B, we must decide how to route a vehicle (or vehicles) from point A to point B. Given a map of all route choices between A and B we can create a network representing these choices. The problem then reduces to the problem of finding the shortest path in the network from point A to B. This is a well solved problem that can use Dijkstra’s Algorithm for quick solution of small to medium (several thousand nodes) sized problems. 2 Fusun Ulengin
An example for shortest path problem Lets analyse how the solve the problem given in the next slide 3 Fusun Ulengin

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84 mn 132mn 126mn 48mn 120mn 66mn 132mn 156mn 348mn 138mn 90mn 60mn 90mn 84mn 48mn 150mn 126mn A D B C E F I G H j 4 Fusun Ulengin
Dijkstra’s Algorithm: We are given a network represented by links and nodes, where the nodes are connecting points between links, and the links are the costs (distances, times or a combination of both formed as a weighted average of time and distance) to traverse between nodes Initially all the nodes are considered to be unsolved, that is, they are not yet on a defined route A solved node is on the route. Starting with the origin as a solved node. Objective of the nth iteration : Find the nth nearest node to the origin. Repeat for n= 1,2,. .. Until the nearest node is the destination Input for the nth iteration. (n-1) nearest nodes to the origin, solved for at previous iterations, including their shortest route and distance from the origin. These nodes, plus the origin, will be called solved nodes, the others are unsolved nodes 5 Fusun Ulengin

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Dijkstra’s Algorithm: Candidates for the nth nearest node . Each solved node that is directly connected by a branch to one or more unsolved nodes provides one candidate-the unsolved node with the shortest connecting branch. Ties provide additional candidates Calculation of nth nearest node. For each such solved node and its candidate, add the distance between them and the distance of the shortest route to this solved node from the origin. The candidate with the smallest such total distance is the nth nearest node (ties provide additional solved nodes) and its shortest route is the one generating the distance. See the distributed sheet for the manual solution of the problem 6 Fusun Ulengin
How to Solve the Shortest Path Problem Using LOGWARE? You have to use the ROUTE MODULE of LOGWARE the student version of which is given at Ballou (1999) Enter the X and Y coordinates as well as the distances in between each pair of nodes The solution is given in the next slide 7 Fusun Ulengin

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8 Fusun Ulengin
SHORTEST ROUTE METHOD SOLUTION RESULTS Origin node number = 1 Number of nodes = 10 Number of arcs = 17 Shortest paths from origin node 1 to all destination nodes Cost Path 90.00 1 -> 2 138.00 1 -> 3

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## This note was uploaded on 11/10/2009 for the course LOGISTICS 20091 taught by Professor Fusunulengin during the Spring '09 term at Istanbul Technical University.

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9Vehiclerouting2009 - Prof.Dr Fsun lengin Fusun Ulengin 1 Vehicle Routing Separate single origin and destination Once we have selected transport

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